Question

You are considering purchasing one of two assets. Asset 1 has payments of 5,000 at the end of year 1, 10,000 at the end of year 3, and 15,000 at the end of year 5. The price for Asset 1 today is 26,000. Asset 2 has payments of 12,000 at the end of year 4 and 20,000 at the end of year 5. The price of the asset 3 years from now is 29,500. If the current spot curve is below, what is the one year forward rate, deferred three years? Term 1 2 3 4 5 Spot Rate 3.00% 3.40% s3 s4 4.25%

Answer 1

Answer:

hello attached below are the missing option related to your question

5.45% ( D )

Explanation:

Given data:

for asset 1

cost of asset = $26000

Year 1  payments = $5000, year 3 = $10000, year 5 = $15000

For asset 2

cost of asset 2 three years from now  = $29500

year 4 payments = $12000, year 5 payments = $20000

Calculate the one year forward rate deferred three years

find the value of  $(1+s3)^3$ using asset 1

2600 (cost of asset now )  = 5000/ (1.03 +10000) / ((1 +s3)^3 +15000))/ 1.0425^5

from the above equation

(1 +s3)^3 = 1.11559

Now to get the one year forward rate deferred three years we determine that value using asset 2

29500 = 12000 / (1+1 year rate deferred for 3 years) + 220000/(1.0425^5/(1+s3)^3)

hence ( 1 + 1 year rate deferred for three years )

= 12000/(29500-20000)/(1.0425^5)*1.11559)

= 12000/(9500)/(1.0425^5)*1.11559

1 year rate deferred for three years = 5.447% ≈ 5.45%